The Search for Mathematical Roots, 1870-1940

Rating:
Summary: The best book of its kind in existence
Review: I have owned a copy for over a year, and not a week goes by in which I do not consult it. The bibliography alone is worth the price.

Modern foundational mathematics emerged around 1840, with the work of Boole, De Morgan, and Bolzano. In the 1870s, Cantor, Peirce, Frege made their appearance. In the 1890s, Peano, Hilbert, Russell and Whitehead came on line. The author is an authority on Cantor, the rise of set theory, on Russell, and Principia Mathematica, and these are covered in great detail. The era closes in the 1930s, with the negative metatheorems of Goedel and Church, and the rise of Quine. All this makes for an exciting human adventure, and this book is the best narrative we have of that adventure.

The book is a gold mine of details little known to most philosophers and to nearly all mathematicians. Here I learned that Husserl was trained as a mathematician, and that much of foundational mathematics can be seen as reflections on Kant. I should grant that IGG is not fair to everyone: Skolem, for instance, is slighted. Also, this book is far from definitive about Polish logic, which deserves a book of its own. Watch for the coming biography of Tarski.

Rating:
Summary: Not what you might expect
Review: I hoped that reading this book would give me a better understanding, in an historical context, of the issues involved in the controversies about the foundations of mathematics a century ago. I found this book fairly interesting, and it was a quick read, but it seems to be written for those who already have an essentially complete understanding of those issues, since the ideas themselves were addressed only tangentially. The focus of the book is much more on: who published what paper when, to what journal did he send it, who was the editor of the journal, who refereed the paper, to whom were offprints sent, in what archives can the manuscript be found, who read whose paper when, who met whom at what conference, who used what notation in writing which paper. This is very much a documentary history, and historians of mathematics will probably love it, but I am probably not the only mathematician who will not find this book completely satisfying.